The town Ukraine says Russia targeted - Marhanets - is one Moscow says its foes have used in the past to shell Russian soldiers at the Zaporizhzhia plant, which they seized in March.
President Volodymyr Zelenskiy said Ukrainian forces would respond to the shelling of Marhanets.
Ukraine's military said Russia also bombarded several other areas in the Zaporizhzhia region including the coal-mining town of Vuhledar.
Calling on foreign allies to send more powerful weapons, Zelenskiy said in a late-night video address Kyiv "will not leave today's Russian shelling of the Dnipropetrovsk region unanswered".
Ukrainians and the country's allies must think about "how to inflict the greatest possible losses on the occupiers in order to shorten the war", he said.
Ukraine and Russia have accused each other of imperilling the plant, Europe's largest nuclear complex, with attacks nearby.
After the United Nations atomic energy watchdog sounded the alarm over a potential nuclear disaster, the Group of Seven leading industrialised countries on Wednesday told Russia to hand back the plant to Ukraine.
There were no indications their demand will sway Moscow, which on Wednesday received powerful endorsement from China of its rationale for the February 24 invasion of Ukraine.
Beijing's ambassador to Moscow, Zhang Hanhui, accused Washington of backing Russia into a corner with repeated expansions of the western-led NATO military alliance and support for Ukraine's alignment with the European Union.
Washington's "ultimate goal is to exhaust and crush Russia with a protracted war and the cudgel of sanctions", Zhang was quoted as saying.
Russia has not commented on the Ukrainian allegations of an attack on Marhanets and Reuters could not independently verify Kyiv's version.
Andriy Yermak, Zelenskiy's chief of staff, said Russia was launching attacks with impunity from Zaporizhzhia knowing it was risky for Ukraine to fight back.
"The cowardly Russians can't do anything more so they strike towns ignobly hiding at the Zaporizhzhia atomic power station," he said on social media
Ukraine says around 500 Russian troops with heavy vehicles and weapons are at the plant, where Ukrainian technicians continue to work.
Ukraine's state nuclear power firm has warned containers with radioactive material might be shelled and said it is vital Kyiv retake the plant by winter.
It accuses Russia of wanting to connect the facility to its power grid.
Russia says its forces are behaving responsibly and ensuring the complex's safety.
Valentyn Reznychenko, governor of Ukraine's central Dnipropetrovsk region, said more than 20 buildings had been damaged in the town on the other side of the Dnipro river from the power plant.
Images supplied by Ukrainian officials showed the rubble-strewn corridor of a school with its windows blown out and a residential building pierced by a rocket.
Moscow pressed its campaign on multiple fronts on Wednesday.
Ukraine's military reported Russian forces shelled some 28 towns in the northeast, southwest and south including the Kharkiv, Donetsk and Kherson regions.
Ukraine's general staff said in an unverified statement Ukrainian counterattacks forced Russian troops to retreat in most of them.
The war has crushed Ukraine's economy, but there was some relief on Wednesday when overseas creditors backed Kyiv's request for a two-year freeze on payments on almost $US20 billion ($A28 billion) in international bonds. That should avert a messy default.
As Kyiv hailed the move as a sign of solidarity by private investors abroad, Ukrainian Prime Minister Denys Shmyhal said the deal would save his country almost $US6 billion.
"These funds will help us maintain macrofinancial stability, strengthen the sustainability of the Ukrainian economy and improve the power of our army," he said.
In another rare positive for Ukraine, the United Nations said it expects to see a big uptick in applications for ships to export its grain under a mediated deal intended to unblock exports and ease global shortages and price hikes.
